Simple description of bipolar transistors:

For switching behavior ... Pull the BASE toward the COLLECTOR to "turn it on." Pull the BASE toward the EMITTER to "turn it off."

As the base voltage is increased beyond the base-emitter junction's forward voltage, to be found in the transistor's datasheet, but generally on the order of ~0.68 volts, the transistor begins to conduct from collector to emitter. You'll be operating the transistor as a switch, i.e. the control voltage applied at the base will switch from nearly Vcc to nearly Gnd.

If you apply a voltage at the base when the transistor is conducting, the voltage between the base and the emitter remains more or less constant. As a result, you can calculate the emitter current, which is the sum of the base current and the collector current (pay attention to the sign!) using Ohms Law if you have a resistor at the emitter.

If you just use NPN transistors, driving the anodes will cost you the forward voltage from the supply. If you use NPN transistors with emitters grounded to drive the cathodes, the lowest voltage to which you can drive that cathode is one forward voltage above GND. The LED doesn't care about the voltage, but, rather is very concerned about the current you run through it. Too little, and, well, you won't see much light. Too much and, well, POOF! This holds, generically, whether the voltage is just barely enough to forward-bias the LED or whether it's quite high. That's why you have to be aware of the associated arithmetic. If you fuse one segment, well, the thing won't work any longer.

If you look at the supply voltage at which the original device from which you got the LED array came, determining its supply voltage and looking at any resistors used in conjunction, you can use that information as a "ball-park" guess as to how much current a segment can tolerate. That way, you can prevent destructive trials. Most LED's visible from across a dark room can tolerate between 10 and 20 mA. Some will tolerate quite a bit more for a short time (10 ms) but won't "like" that same current for more than 1 second. LED's generate a moderate amount of heat. With too much current, it becomes too much heat, and that will likely damage the LED. Be careful! Once you've figured out to what value you should limit the current to each segment, you can do that and rest assured you won't break anything. Remember, Ohm's Law is your friend.

The trick with LED's, in general, is to light a few segments at a time, but do so at a rate that will cause the human observer to see all the lighted segments as though they were constantly "on".

RE